I was in Alaska in June using a prepaid T-mobile. It will roam to another network, don't remember which one. Coverage as expected was good in some areas, not even one bar in many others. You probably won't be able to call out of the country without using a calling card on a prepaid account, but that's way less money anyways.

On the ship it may not work if they have one of those insanly priced systems, but in port cities you should be fine. T-mobile sims are all over the internet, very little money, it's possible somebody will be willing to ship it to your hotel in fairbanks.